using integration by parts to hate myselfpic.twitter.com/mLwr37sHfU
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Hey, I'll use this in the calculus class I'm teaching this quarter, as an early example of integration by parts. They'll like it!
funny story .. my friend was trying to troll me one night and just blurted out "prove integral x^n from IBP" (he does stuff like this all the time) i thought about it for a second and went wait.. and when i saw it worked i died laughing
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Basically the reason this works (and I think I’m recalling this correctly) is because you‘re secretly deriving the taylor polynomial. In your case, the expansion terminates because the function was a polynomial to begin with.
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the taylor polynomial of x^n is x^n though? there's no expansion here
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